Cubes and Squares

There are two whole numbers,difference of their squares is a cube and difference of their cubes is a square.

These are the smallest possible numbers.

8 comments:

Kannappan said...

The only clue I got till now is that atleast One of the two numbers cannot be below 1000.

Kannappan said...

Provided the question isnt a riddle ^_^)

Kannappan said...

The scripts started consuming 45% cpu when wanted to check for numbers upto 10000. Otherwise it was quite normal.

Senthil Kumaran said...

!riddle

Kannappan said...

hey, atleast one of the answers will be grater than 10,000. What do u say ???

Senthil Kumaran said...

Frankly speaking,me too working on this.this should not be a difficult problem as it seems.

Kannappan said...

Hey hey hey ...A big mistake in my script...which I just now noticed...Oh GOd...teh anwer is simple 6 and 10...
The problem in the first script is the assigning of the variable $a=20....I just changed it to 100...So that we can compare the diferenc of the cubes to upto square of 100.....

The difference between cubes of 6 an 10 leads to 784 whose square root is 48. In my script i compared only till 20 :(

So All the previous results die here...
The Answer is 6 and 10...And hey I havent seen the answer as yet...for my 2 secs of fame that is :)

Kannappan said...

Using Brute Force and a comp program, the olympiad problem is solved as (1,1) (16,2) (27,3) for (a,b). Cant identify any pattern and dunno as yet how to solve it by hand.